Honestly this could just be speaking to some niche desire to have a traditionally femme but still awful name as though it were assigned to you by your parents. Being like "Please, call me Millie, my real name is Mildred (ugh)" definitely lends an air of legitimacy to the whole thing. And it's a classic real world experience of many cis women.
That's just a guess though, more power to her either way, maybe she just thinks Mildred is a rad name. At the end of the day my opinion means jack and/or shit so do what you want.
This is not a unique problem, as California history teems with lesbians changing their name to Morgana Labiablossom or Neopagans to Bridget Oaksparkle when when they cross a personal reckoning. Since it's super important to them, we practice in front of a mirror until we can say the name without giggling.
I wonder if that is what inspired Tungsteena Zarpedon.
I'm really showing my age, but that name brings up fond memories of Fairuza Balk as Mildred Hubble in The Worst Witch (watch it if you get a chance, not only Fairuza, but also Charlotte Rae and Tim Curry, great film, one of my childhood favourites!). (E: omg omg omg it's on youtube!!! I know what I'm watching tonight!)
I see no problem here.
Also Millie for short is cute.